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How to Solve a Diophantine Equation

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An Invitation to Mathematics
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Abstract

We introduce Diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal’s Triangle with state-of-the-art methods.

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References

  1. Michael Beck, Eric Pine, Wayne Tarrant, and Kim Yarbrough Jensen, New integer representations as the sum of three cubes. Mathematics of Computation 76(259), 1683–1690 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, and Szabolcs Tengely, Integral points on hyperelliptic curves. Algebra & Number Theory 2(8), 859–885 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. David Hilbert, Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Congress zu Paris 1900 (German). Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen 1900, 253–297 (1900)

    Google Scholar 

  4. David Hilbert, Mathematical problems. Bulletin of the American Mathematical Society 8, 437–479 (1902); reprinted: Bulletin of the American Mathematical Society (New Series) 37, 407–436 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Marc Hindry and Joseph H. Silverman, Diophantine Geometry. An Introduction. Graduate Texts in Mathematics, volume 201, Springer, New York (2000)

    MATH  Google Scholar 

  6. Yuri V. Matiyasevich, Hilbert’s Tenth Problem. MIT Press, Cambridge (1993)

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  7. Roel J. Stroeker and Benjamin M.M. de Weger, Elliptic binomial Diophantine equations. Mathematics of Computation 68, 1257–1281 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Michael Stoll .

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© 2011 Springer-Verlag Berlin Heidelberg

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Stoll, M. (2011). How to Solve a Diophantine Equation. In: Schleicher, D., Lackmann, M. (eds) An Invitation to Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19533-4_2

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